# Mathematical method for inteligent cargo

Discussion in 'Stability' started by Tcubed, Oct 30, 2013.

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### TcubedBoat Designer

In the general case where all the masses in a boat are in rigid positions w.r.t. the whole boat, the condition for positive small angle stability is G below Z. If G is at Z the boat becomes ambivalent about staying upright, above this and the boat flops over to the angle of LOL or goes 180, or becomes a victim of downflooding.

This changes if the weight is alive and able to compensate for heel angles.

In this case it is possible to have total G above Z and with a bit of care it stays up. I will assume that we restrict the case here for boats whose hulls have a G low enough to stay upright when empty, but that when a (or several) humans get into into it the total G will inevitably be moved upwards.

I do not normally bother with stability calcs for small slender hulls where humans are a significant or major portion of the total mass, prefering to design by experience and precedent.
However , i am now being asked for these calcs...

I designed a fairly conservative (for general public use) but still reasonably shaped canoe which i know just by looking at it will be fine provided you don't dump in two elephants and a baboon, but.... when i do the calcs, by assuming the three maximum and average humans are seated in the ordinary and correct positions, frozen stiff in position,......horror! The total G is above the Z! (just a couple cM)

Even reasonably conservative shapes can end up like so, and yet they do work , even without trained crew..

What gives?

Does anyone know of already established guidelines for ranges of negative GZ for family, ordinary, athletic, profesional which work in practice?

Or does anyone have a reccomendation for altering the calcs that does a roughly good estimate of the effective G, knowing that sentient humans are neither loose ballast , nor frozen stiff?...

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### TcubedBoat Designer

One approach that seems to be possibly realistic is to place each human's CG rigidly at the CL, but instead of around the navel, put it actually on the surface of the corresponding thwart.
This would lower it by approximately 30 cM or so, and may be a realistic approximatnion if one assumes that each human will keep their upper body upright, independently from the boat...

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### ancient kayakeraka Terry Haines

Mostly I design solo canoes and I am comfortable with the metacenter 35 cm or so above the keel, since in a solo canoe with the paddler sitting on the bottom his/her center of gravity is typically 20cm above keel for a GM of about 15cm so it is moderately stable, tippy so it allows waves to pass without much rocking. My canoes are so light <10Kg their center of gravity has little effect.

A more recent design is longer - 4.88m but still quite slim - 79cm beam. For that design the metacentric height is 50cm solo which reduces to 42.5cm with two on board. This illustrates the effect of increasing the load. With this canoe the seat height is about 20 cm and the center of gravity of a paddler on a raised seat is lower. I estimate that puts the GM about 20cm above the keel for excelent stability by solo canoe standards, but with two paddlers the CM would be reduced to about 12.5cm, less than my solo canoes typically provide, so it would be a nervous boat for two unless experienced.

The design is an interesting one, based on a Walter Dean canoe around 1915 I believe. It was often paddled solo, and was popular for women who no doubt appreciated the good solo stability. However it was occasionally equipped as a "girling" canoe, the canoe of choice for young men to entertain their girlfriends in those far-off days. The stability problem was solved, I assume, in the design of the bow seat provided for the young lady, which I suspect was very low, and pictures show it was reclined so the lady's center of gravity was kept low. One presumes no respectable lady would risk a ducking back then so something of the kind had to be . . . with the long dresses of the day they would have been in danger of drowning!

I used to have an old fiberglass canoe, 4.3m x 91cm, quite beamy. Strangely it wasn't especially stable even for solo paddling and only felt stable with two up if both sat perfectly still. When I took it out with an inexperienced but enthusiastic paddler as crew, who flailed away in the bow with little regard for keeping the boat dry and upright. I was quite nervous, I thought it was going to tip. I don't have the metacentric data for that boat but it should have been considerable, but it never felt like a comfortable boat, even when I was kneeling. I have a small kayak with a 76cm beam, wide by kayak standards but narrower than the old canoe, and it is absolutely solid, I can lean far over the side to wtch the fishes without fear of tipping. There is more to stability than the metacenter.

The problem is, when the second paddler gets on board the metacenter M moves down and the center of gravity G moves up - though not by much for a lightweight boat - so the metacentric height GM is reduced significantly.

Calculation of the center of gravity G requires proper data for the human body. When seated flat on the floor it is about 20cm from the floor, and on a seat raised above the floor it is higher but not by as much as the seat because most of heavy legs remain lower than the seat. There should be anthropomorphic data on the web.

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### TANSLSenior Member

Tcubed do not know if I understand correctly but I think it is impossible that G is below Z. It all depends, of course, on where you've placed the baseline. Perhaps if you attach a picture of the canoe could study what happens to you.

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### TcubedBoat Designer

AK, thanks for those data.

Here are the specs;
LOA 5.65 M
Beam 0.89 M
beam at chine 0.75
Empty weight 53 kg
designed for 1, 2 or 3 people.

I wanted to make it longer but my client reminded me of the road legal overhang restrictions so i had to shorten it a bit, so it could be car toppable on a reasonably big car or pickup.

The CG of a standing human is reliably at the navel, at about half abdomen thickness.
Legs comprise ~1/3 total body mass, sitting legs flat on the floor will move the CG up and forward to almost 10 cM up and forward of the navel, putting the CG a good 30 cM up from the seat of pants, lowering legs slightly below seat will bring it back down but it will still be closer to 30 cM above seat.

Girling boats nowadays are almost always speedboats or muscleboats (obviously) or for the real knuckleheads; jetskis,...
although i must say i myself have bucked the trend and had quite a bit of success with smart pulling boats, which if played right can absolutely ooze romantic sophistication........... but only if you know how to row!!! (which of course almost no one knows anymore)

Tansl , the metacenter's position will be at a certain height w.r.t. to the boat, the same as the CG, irrespective of baseline. Baseline is completely arbitrary. And yes, it is possible for metacenter Z to be below G precisely because the cargo is sentient. This is precisely the nature of my question;

What are acceptable ranges for different levels of experience ?
For example racing kayaks are normally so unstable that you will capsize no matter your skill level if you do not have the paddle to use to push on the water with. ie severely negative GZ. Of course that is not what i'm aiming for here,i'm instead trying to push the envelope for average people and i wonder how far is still acceptable.

First image shows the position of Z at different loadings, as expected it moves down as the immersed sections become deeper but barely any wider.
Worst case with 3 people and if the humans are frozen solid it means the GZ is almost vanishing. With two people there is still a healthy GZ.
I calculated Z @ 1 degree of heel. If i repeat at 5 degrees the values are almost the same as expected since it is within the linear portion of the righting moments graph. Minor grid lines at 10 cM , major at 1 M.

Second image shows that it is not very extreme, but neither is it a bathtub like most commercial canoes. Third is general view . Last image shows different WL and dims. For initial stability it is the width at the bottom that counts (actually it is the transversal area moment of inertia of the waterplane).

The whole thing is made out of 2 mM welded aluminium , 4 folded strips make the stringers for bottom stiffness, seats same and filled with foam 9cM thick just enough to keep it from going to the bottom if boat flooded. All panels are developable with a maximum gaussian curvature of -2x10^-6 M .

My aim here is to create the best performance possible but still be accesible to average people (not lard sacks, but not necesarily athletic either) and i wonder whether treating people as if they were frozen stiff is an excessive stability criterion. I am beginning to really think that putting the effective CG of each human on the surface of each thwart is actually an acceptable approximation of real human behavior. Any thoughts on this?

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### TcubedBoat Designer

Yes Z is metacenter

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### TcubedBoat Designer

Sorry yeah you are right M is the usual symbol for that. I work on my lonesome so i tend to drift away unwittingly from conventions..

I'll open that pdf now

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### TcubedBoat Designer

The thing is all these calcs necessarily treat the humans body mass as something that is rigid, which is no longer a valid assumption once the human payload is majority fraction of total displacement.
If the boat heels, most people will automatically adjust to stay upright, (not stay frozen stiff!) therefore creating a dynamically changing total CG, which is practically impossible to model.
So instead i'm trying to see what can be used as an alternative simplifying CG modeling assumption that will mimic human behaviour.

Like i said i think this means treating each persons CG as being lower than it actually is... otherwise a lot of these canoes would be unusable.

Active roll stabilization is a powerful method but will not be used by average people. I once had the opportunity to try a racing kayak which was about 20 cM wide at the WL. Wow! that was nervy, but with the paddle you could stay up. I reached 7.5 knots but a pro can go above 10 with a thing like that.

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### DCockeySenior Member

PDF? What PDF are you referring to?

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### DCockeySenior Member

Documents?

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### TANSLSenior Member

Tcubed, I do not know what you need and although I´d like to help I can not understand anything. You start to use a different nomenclature that I use. For you Z is the metacentre and G, what is?. On the other hand it seems you're talking to a ghost that only you are able to hear. Are you interested in getting help from humans?.
The cog of a seated person is between 5 and 10 cm above the seat

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### TcubedBoat Designer

Soz for rambling .

The documents i was reffering to are in the link that AK posted above.
Wait, that is strange, the link is not there anymore..?? weird

http://www.boatdesign.net/forums/bo...culation-implications-30857-9.html#post353422

My bad, Z is not standard symbol as AK pointed out. It should be M , M for Metacenter. Will use M from now on.
And G is center of mass, yes.

To re iterate my question which i no doubt did not make clear enough;
It seems to me that the normal G below Z condition breaks down once a significant portion of the total mass is human.
ie there are boats that one would think would be unusable but are in fact fine, since humans are constantly compensating for slight instabities.
Therefore i was wondering if there are any alternative protocols for establishing acceptable stability in slender boats which are light compared to the pasengers.
Like for example , pretending that the CG of each human is at an established height that does a satisfactory job of predicting how nervous the boat will be in practice.

Tansl, how do you get CG of seated person between 5 and ten cM above seat? It seems to me that it should be higher , especially if the legs are more or less outstretched in front.

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### TANSLSenior Member

The standards for passenger ships say that for stability calculations the cog of the passenger, sitting, is 60 cm from the ground. Therefore I say that should be between 5 and 10 cm above the seat, but you put whatever you want.
As for stability, I do not know if it seems like a silly thing, but the bilge keels greatly reduce the roll of the ship, increasing very little weight.

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### ancient kayakeraka Terry Haines

I don't have experience with vee-bottom designs so I can't say how that design will behave in the water. The hard chines will tend to dampen out rolling, like the bilge keels that TANSL referred to

I do not like the transom which is dragging in the water. That will be a source of drag and noise. The only use for a transom on a canoe is for a motor surely, but if you need one, look at some rowboat designs for ideas on it can be done.

The classic wineglass transom preserves the slick underwater shape of a canoe or rowing shell while providing the desired space in the stern, but it is not an easy thing to build. An easier approach is to flatten the bottom approaching the stern and curve the bottom so it's at the waterline with the max load; that adds reserve buoyancy at the stern for an outboard without making the boat a cow to paddle or row. The only boat of mine that had a transom was flat-bottomed, much easier but a whole different thing from your canoe.

Does your design application provide cross-curves? They are probably the most useful thing for predicting heeling behavior.

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### TcubedBoat Designer

That is a necessary compromise so that a small outboard can be used. In practice, a bit of immersed transom is not as bad as one might think because it allows the lines from midsection aft to be straightened out, which compensates substantially for the turbulence of the wet transom. Of course for paddling it is not the best, but like i said people will be using it with an outboard mostly (i mean lets get real; who paddles nowadays?) so i had to compromise, whilst still trying for ok paddling.

Compromises, compromises....

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